Uninorms Having an Identity and an Annihilator on Bounded Lattices

Yıl 2019, , 344 - 352, 15.04.2019

Gül Deniz Çaylı

https://doi.org/10.17714/gumusfenbil.435836

Öz

Uninorms defined on bounded lattices are an
important generalization of triangular norms and triangular conorms and these
operators allow the identity to be any point in a bounded lattice. In this
study, uninorms on bounded lattices are studied. It is proposed a method to
characterize uninorms on bounded lattices having an identity and an annihilator
on bounded lattices and some basic properties of such uninorms are investigated.
Moreover, an example is provided to illustrate the feasibility of the proposed
method.

 

Anahtar Kelimeler

Identity, Annihilator, Bounded lattice, Uninorm

Sınırlı Kafesler Üzerinde Bir Birime ve Bir Sıfırlayana Sahip Uninormlar

Öz

Sınırlı kafesler üzerinde
tanımlanan uninormlar, üçgensel normların ve üçgensel konormların önemli bir
genelleştirmesidir ve bu operatörler, birimin sınırlı kafesin herhangi bir
noktasında olmasına olanak sağlarlar. Bu çalışmada, sınırlı kafesler üzerinde
uninormlar konusu üzerine çalışılmıştır. 
Sınırlı kafesler üzerinde bir birime ve sıfırlayana sahip uninormları
karakterize etmek için bir metot önerildi ve bu şekildeki uninormların bazı
temel özellikleri araştırıldı. Ayrıca, önerilen metotun uygulanabilirliğini
göstermek için bir örnek verildi.   

 

Anahtar Kelimeler

Birim, Sıfırlayan, Sınırlı Kafes, Uninorm

Kaynakça

• Aşıcı, E. and Karaçal, F., 2016. Incomparability with respect to the triangular order. Kybernetika, 52, 15-27.
• Aşıcı, E., 2017. An order induced by nullnorms and its properties. Fuzzy Sets and Systems, 325, 35-46.
• Aşıcı, E., 2018. Some remarks on an order induced by uninorms, in: Kacprzyk, J., et al. (Eds.) Advances in Fuzzy Logic and Technology, Advances in Intelligent Systems and Computing, Springer, Cham, 641, 69-77.
• Beliakov, G., Pradera, A. and Calvo, T., 2007. Aggregation Functions: A Guide for Practitioners, Berlin, Springer 374p.
• Birkhoff, G., 1967. Lattice Theory: American Mathematical Society Colloquium Publishing, Providence, RI, 418p.
• Bodjanova, S. and Kalina, M., 2014. Construction of uninorms on bounded lattices. IEEE 12th International Symposium on Intelligent Systems and Informatics, SISY 2014, 11-13 September 2014, Subotica, Serbia, pp. 61-66.
• Çaylı, G.D., Karaçal, F. and Mesiar, R., 2016. On a new class of uninorms on bounded lattices. Information Sciences, 367-368, 221-231.
• Çaylı, G.D. and Karaçal, F., 2017. Construction of uninorms on bounded lattices. Kybernetika, 53, 394-417.
• Çaylı, G.D. and Drygaś, P., 2018. Some properties of idempotent uninorms on a special class of bounded lattices. Information Sciences, 422, 352-363.
• Çaylı, G.D., 2018. On a new class of t-norms and t-conorms on bounded lattices. Fuzzy Sets and Systems, 332, 129-143.
• Çaylı, G.D., 2018. Uninorms that are neither conjunctive nor disjunctive on bounded lattices, in: Medina, J., et al. (Eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems, Communications in Computer and Information Science, Springer, Cham, 853, 310-318.
• De Baets, B. and Fodor, J., 1999. Van Melle's combining function in MYCIN is a representable uninorm: an alternative proof. Fuzzy Sets and Systems, 104, 133-136.
• Drewniak, J. and Drygaś, P., 2002. On a class of uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 10, 5-10.
• Drygaś, P., 2004. Isotonic operations with zero element in bounded lattices, in: Atanassov, K., (Eds.) Soft Computing Foundations and Theoretical Aspect, EXIT Warszawa, p. 181-190.
• Drygaś, P., Qin, F. and Rak, E., 2017. Left and right distributivity equations for semi-t-operators and uninorms. Fuzzy Sets and Systems, 325, 21-34.
• Fodor, J., Yager, R.R. and Rybalov, A., 1997. Structure of uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5, 411-427.
• Gabbay, D. and Metcalfe, G., 2007. Fuzzy logics based on [0, 1)-continuous uninorms. Archive for Mathematical Logic, 46, 425-449.
• Grabisch, M., Marichal, J.L., Mesiar, R. and Pap, E., 2009. Aggregation Functions: Cambridge, Cambridge University Press, 482p.
• Karaçal, F. and Mesiar, R., 2015. Uninorms on bounded lattices. Fuzzy Sets and Systems, 261, 33-43.
• Mesiarová-Zemanková, A., 2015. Multi-polar t-conorms and uninorms. Information Sciences, 301, 227-240.
• Tsadiras, A.K. and Margaritis, R.G., 1998. The MYCIN certainly factor handling function as uninorm operator and its use as a threshold function in artificial neurons. Fuzzy Sets and Systems, 93, 263-274.
• Yager, R.R. and Rybalov, A., 1996. Uninorms aggregation operators. Fuzzy Sets and Systems, 80, 111-120.
• Yager, R.R., 2001. Uninorms in fuzzy systems modeling. Fuzzy Sets and Systems, 122 (1), 167-175.
• Yager, R.R., 2003. Defending against strategic manipulation in uninorm-based multi-agent decision making. Fuzzy Sets and Systems, 140, 331-339.
• Yager, R.R. and Kreinovich, V., 2003. Universal approximation theorem for uninorm-based fuzzy systems modeling. Fuzzy Sets and Systems, 140, 331-339.